Have each student choose one president in history and research and write a biography of him. You can also assign a president to each student. Instruct students to research his life and what went on in his time in office. Tell students to write about what distinguished their president from the others, including what was going on in the world during his tenure and how he affected it. Have students find a picture of their president and present their findings to the class.
The office of the president is unlike any other. Have students research what the president's precise role is in government. Most of them probably don't know that the president cannot actually propose legislation. Have them find out what the president can and cannot do. For a more ambitious project, ask students to research how the role of the president, and his powers, have changed over time. As a creative add-on to this exercise, have the class come up with a job description for president.
This activity forces students to research a number of different presidents in history. Ask students to use research to determine who the best president ever was. Have them consider what kinds of obstacles past presidents faced and how they met the challenges that faced them. Students will probably come up with differing opinions. For a presentation component, allow students to stage a debate about who the best president is.
The system for electing the U.S. President is rather unique. Students probably don't know of the existence of the electoral college, never mind how it works. Ask students to research how a president gets elected, from party primaries all the way to election day. Once students have completed their research, you can put it into practice by staging your own presidential election. Mimic the real system as much as possible to elect a class president and show your students how the electoral system actually works.